Journal of East China Normal University(Natural Sc ›› 2014, Vol. 2014 ›› Issue (1): 36-46.

• Article • Previous Articles     Next Articles

Determining the topology of real intersection of algebraic surfaces

GAO Ben1,  CHEN Yu-fu2   

  1. 1. College of Mathematics, Taiyuan University of Technology,  Taiyuan 030024, China;
    2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2013-01-01 Revised:2013-04-01 Online:2014-01-25 Published:2015-09-25

Abstract: This paper gave an algorithm for computing in an efficient
way the topology of the real intersection of algebraic surfaces,
which are defined by a finite family of trivariate polynomials with
coefficients in $\R$. The algorithm is based on the computation of
the graphs which are the intersection of at most two projections.
For this purpose, some conditions, which be obtained by some
linearly change of coordinates were fultiued, and some methods for
checking these conditions were presented.

Key words: algebraic surface, generic position, topology, subresultants sequence

CLC Number: